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Confidence-Interval Coverage
One hundred intervals from one hundred samples: count how many catch the true mean.
Day 9: Confidence Intervals & the BootstrapCovered (of 100)
97
Long-run coverage
94.3%
3,000 more samples; nominal 95%
Critical value
2.093
t, df = 19
Try n = 5 with the z value: coverage falls short. Then try skewed data with small n.
Each horizontal line is a confidence interval from a new sample. The true mean (dashed) never moves; the intervals do. Orange intervals miss it.